EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2014-026 LHCb-PAPER-2014-001 27 February 2014
Observation of photon polarization
in the b → sγ transition
The LHCb collaboration†
Abstract
This Letter presents a study of the flavor-changing neutral current radiative B±→ K±π∓π±γ decays performed using data collected in proton-proton collisions with the LHCb detector at 7 and 8 TeV center-of-mass energies. In this sample, corresponding to an integrated luminosity of 3 fb−1, nearly 14 000 signal events are reconstructed and selected, containing all possible intermediate resonances with a K±π∓π± final state in the [1.1, 1.9] GeV/c2 mass range. The distribution of the angle of the photon direction with respect to the plane defined by the final-state hadrons in their rest frame is studied in intervals of K±π∓π± mass and the asymmetry between the number of signal events found on each side of the plane is obtained. The first direct observation of the photon polarization in the b → sγ transition is reported with a significance of 5.2 σ.
Published in Phys. Rev. Lett. 112, 161801 (2014)
c
CERN on behalf of the LHCb collaboration, license CC-BY-3.0.
†Authors are listed on the following pages.
LHCb collaboration
R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P. Alvarez Cartelle37, A.A. Alves Jr25, S. Amato2, S. Amerio22, Y. Amhis7, L. Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E. Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A. Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,m, M. Baalouch5, S. Bachmann11, J.J. Back48, A. Badalov36, V. Balagura31, W. Baldini16, R.J. Barlow54, C. Barschel39, S. Barsuk7,
W. Barter47, V. Batozskaya28, Th. Bauer41, A. Bay39, J. Beddow51, F. Bedeschi23, I. Bediaga1, S. Belogurov31, K. Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson50,
J. Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47, M. van Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M. Bjørnstad54, T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30, W. Bonivento15,38, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E. Bowen40, C. Bozzi16, T. Brambach9, J. van den Brand42, J. Bressieux39, D. Brett54, M. Britsch10, T. Britton59, N.H. Brook46, H. Brown52, A. Bursche40, G. Busetto22,q, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, O. Callot7, M. Calvi20,k,
M. Calvo Gomez36,o, A. Camboni36, P. Campana18,38, D. Campora Perez38, F. Caponio21, A. Carbone14,d, G. Carboni24,l, R. Cardinale19,j, A. Cardini15, H. Carranza-Mejia50, L. Carson50, K. Carvalho Akiba2, G. Casse52, L. Cassina20, L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, R. Cenci58, M. Charles8, Ph. Charpentier38, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, K. Ciba38, X. Cid Vidal38, G. Ciezarek53, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J. Closier38, C. Coca29, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins38,
A. Comerma-Montells36, A. Contu15,38, A. Cook46, M. Coombes46, S. Coquereau8, G. Corti38, I. Counts56, B. Couturier38, G.A. Cowan50, D.C. Craik48, M. Cruz Torres60, S. Cunliffe53, R. Currie50, C. D’Ambrosio38, J. Dalseno46, P. David8, P.N.Y. David41, A. Davis57, I. De Bonis4, K. De Bruyn41, S. De Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. D´el´eage4, D. Derkach55, O. Deschamps5, F. Dettori42, A. Di Canto11, H. Dijkstra38, S. Donleavy52, F. Dordei11, M. Dorigo39, P. Dorosz26,n, A. Dosil Su´arez37, D. Dossett48, A. Dovbnya43, F. Dupertuis39, P. Durante38, R. Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49, U. Egede53,
V. Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L. Eklund51,38, I. El Rifai5, Ch. Elsasser40, S. Esen11, A. Falabella16,f, C. F¨arber11, C. Farinelli41, S. Farry52, D. Ferguson50, V. Fernandez Albor37, F. Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,f, M. Fiorini16,f, C. Fitzpatrick38, M. Fontana10, F. Fontanelli19,j, R. Forty38, O. Francisco2, M. Frank38, C. Frei38, M. Frosini17,38,g, J. Fu21, E. Furfaro24,l,
A. Gallas Torreira37, D. Galli14,d, S. Gambetta19,j, M. Gandelman2, P. Gandini59, Y. Gao3, J. Garofoli59, J. Garra Tico47, L. Garrido36, C. Gaspar38, R. Gauld55, L. Gavardi9,
E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A. Gianelle22, S. Giani’39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C. G¨obel60, D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, H. Gordon38, M. Grabalosa G´andara5, R. Graciani Diaz36,
L.A. Granado Cardoso38, E. Graug´es36, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P. Griffith45, L. Grillo11, O. Gr¨unberg61, B. Gui59, E. Gushchin33, Yu. Guz35,38, T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, T.W. Hafkenscheid64, S.C. Haines47, S. Hall53, B. Hamilton58, T. Hampson46, S. Hansmann-Menzemer11, N. Harnew55, S.T. Harnew46, J. Harrison54, T. Hartmann61, J. He38, T. Head38, V. Heijne41, K. Hennessy52, P. Henrard5, L. Henry8, J.A. Hernando Morata37, E. van Herwijnen38, M. Heß61, A. Hicheur1, D. Hill55,
M. Hoballah5, C. Hombach54, W. Hulsbergen41, P. Hunt55, N. Hussain55, D. Hutchcroft52, D. Hynds51, M. Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, E. Jans41, P. Jaton39, A. Jawahery58, F. Jing3, M. John55, D. Johnson55, C.R. Jones47, C. Joram38, B. Jost38, N. Jurik59, M. Kaballo9, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38, M. Kelsey59, I.R. Kenyon45, T. Ketel42, B. Khanji20, C. Khurewathanakul39, S. Klaver54, O. Kochebina7, I. Komarov39, R.F. Koopman42, P. Koppenburg41, M. Korolev32,
A. Kozlinskiy41, L. Kravchuk33, K. Kreplin11, M. Kreps48, G. Krocker11, P. Krokovny34, F. Kruse9, M. Kucharczyk20,26,38,k, V. Kudryavtsev34, K. Kurek28, T. Kvaratskheliya31,38, V.N. La Thi39, D. Lacarrere38, G. Lafferty54, A. Lai15, D. Lambert50, R.W. Lambert42,
E. Lanciotti38, G. Lanfranchi18, C. Langenbruch38, B. Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P. Lees4, R. Lef`evre5, A. Leflat32, J. Lefran¸cois7, S. Leo23, O. Leroy6, T. Lesiak26, B. Leverington11, Y. Li3, M. Liles52, R. Lindner38, C. Linn38, F. Lionetto40, B. Liu15, G. Liu38, S. Lohn38, I. Longstaff51, J.H. Lopes2, N. Lopez-March39, P. Lowdon40, H. Lu3, D. Lucchesi22,q, H. Luo50, E. Luppi16,f, O. Lupton55, F. Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30,38, S. Malde55, G. Manca15,e, G. Mancinelli6, M. Manzali16,f, J. Maratas5, U. Marconi14, C. Marin Benito36, P. Marino23,s, R. M¨arki39, J. Marks11, G. Martellotti25, A. Martens8, A. Mart´ın S´anchez7, M. Martinelli41,
D. Martinez Santos42, F. Martinez Vidal63, D. Martins Tostes2, A. Massafferri1, R. Matev38, Z. Mathe38, C. Matteuzzi20, A. Mazurov16,38,f, M. McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. McSkelly52, B. Meadows57,55, F. Meier9, M. Meissner11, M. Merk41,
D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez60, S. Monteil5, D. Moran54, M. Morandin22, P. Morawski26, A. Mord`a6, M.J. Morello23,s, R. Mountain59, F. Muheim50, K. M¨uller40,
R. Muresan29, B. Muryn27, B. Muster39, P. Naik46, T. Nakada39, R. Nandakumar49, I. Nasteva1, M. Needham50, N. Neri21, S. Neubert38, N. Neufeld38, A.D. Nguyen39, T.D. Nguyen39,
C. Nguyen-Mau39,p, M. Nicol7, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A. Novoselov35, A. Oblakowska-Mucha27, V. Obraztsov35, S. Oggero41, S. Ogilvy51, O. Okhrimenko44,
R. Oldeman15,e, G. Onderwater64, M. Orlandea29, J.M. Otalora Goicochea2, P. Owen53, A. Oyanguren36, B.K. Pal59, A. Palano13,c, F. Palombo21,t, M. Palutan18, J. Panman38, A. Papanestis49,38, M. Pappagallo51, L. Pappalardo16, C. Parkes54, C.J. Parkinson9, G. Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, C. Pavel-Nicorescu29, A. Pazos Alvarez37, A. Pearce54, A. Pellegrino41, M. Pepe Altarelli38, S. Perazzini14,d, E. Perez Trigo37, P. Perret5, M. Perrin-Terrin6, L. Pescatore45, E. Pesen65, G. Pessina20, K. Petridis53, A. Petrolini19,j, E. Picatoste Olloqui36, B. Pietrzyk4, T. Pilaˇr48, D. Pinci25, A. Pistone19, S. Playfer50, M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E. Polycarpo2, A. Popov35, D. Popov10, B. Popovici29, C. Potterat36, A. Powell55, J. Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39, G. Punzi23,r, W. Qian4, B. Rachwal26, J.H. Rademacker46, B. Rakotomiaramanana39, M. Rama18, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G. Raven42, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S. Ricciardi49, A. Richards53, K. Rinnert52, V. Rives Molina36, D.A. Roa Romero5, P. Robbe7, D.A. Roberts58, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez37, S. Roiser38,
V. Romanovsky35, A. Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, F. Ruffini23, H. Ruiz36, P. Ruiz Valls36, G. Sabatino25,l, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B. Saitta15,e, V. Salustino Guimaraes2, B. Sanmartin Sedes37, R. Santacesaria25,
C. Santamarina Rios37, E. Santovetti24,l, M. Sapunov6, A. Sarti18, C. Satriano25,m, A. Satta24, M. Savrie16,f, D. Savrina31,32, M. Schiller42, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O. Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18,
A. Sciubba25, M. Seco37, A. Semennikov31, K. Senderowska27, I. Sepp53, N. Serra40, J. Serrano6, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T. Shears52, L. Shekhtman34, O. Shevchenko43, V. Shevchenko62, A. Shires9, R. Silva Coutinho48, G. Simi22, M. Sirendi47, N. Skidmore46, T. Skwarnicki59, N.A. Smith52, E. Smith55,49, E. Smith53, J. Smith47,
M. Smith54, H. Snoek41, M.D. Sokoloff57, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B. Spaan9, A. Sparkes50, F. Spinella23, P. Spradlin51, F. Stagni38,
S. Stahl11, O. Steinkamp40, S. Stevenson55, S. Stoica29, S. Stone59, B. Storaci40, S. Stracka23,38, M. Straticiuc29, U. Straumann40, R. Stroili22, V.K. Subbiah38, L. Sun57, W. Sutcliffe53,
S. Swientek9, V. Syropoulos42, M. Szczekowski28, P. Szczypka39,38, D. Szilard2, T. Szumlak27, S. T’Jampens4, M. Teklishyn7, G. Tellarini16,f, E. Teodorescu29, F. Teubert38, C. Thomas55, E. Thomas38, J. van Tilburg11, V. Tisserand4, M. Tobin39, S. Tolk42, L. Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,53, S. Tourneur39, M.T. Tran39, M. Tresch40, A. Tsaregorodtsev6, P. Tsopelas41, N. Tuning41, M. Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin62, U. Uwer11, V. Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. V´azquez Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h,
G. Veneziano39, M. Vesterinen11, B. Viaud7, D. Vieira2, X. Vilasis-Cardona36,o, A. Vollhardt40, D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß61, H. Voss10,
J.A. de Vries41, R. Waldi61, C. Wallace48, R. Wallace12, S. Wandernoth11, J. Wang59, D.R. Ward47, N.K. Watson45, A.D. Webber54, D. Websdale53, M. Whitehead48, J. Wicht38, J. Wiechczynski26, D. Wiedner11, G. Wilkinson55, M.P. Williams48,49, M. Williams56, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M. Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, S. Wu3, K. Wyllie38, Y. Xie50,38, Z. Xing59, Z. Yang3, X. Yuan3, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b, F. Zhang3, L. Zhang59, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3, A. Zvyagin38.
1Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center for High Energy Physics, Tsinghua University, Beijing, China 4LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy 14Sezione INFN di Bologna, Bologna, Italy 15Sezione INFN di Cagliari, Cagliari, Italy 16Sezione INFN di Ferrara, Ferrara, Italy 17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy 21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy 23Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland 27AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,
Krak´ow, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain 38European Organization for Nuclear Research (CERN), Geneva, Switzerland 39Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 40Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The
Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 48Department of Physics, University of Warwick, Coventry, United Kingdom 49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 51School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States 57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States 59Syracuse University, Syracuse, NY, United States
60Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2 61Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to11
62National Research Centre Kurchatov Institute, Moscow, Russia, associated to31
63Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated to36 64KVI - University of Groningen, Groningen, The Netherlands, associated to41
65Celal Bayar University, Manisa, Turkey, associated to38
aUniversidade Federal do Triˆangulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia cUniversit`a di Bari, Bari, Italy
dUniversit`a di Bologna, Bologna, Italy eUniversit`a di Cagliari, Cagliari, Italy fUniversit`a di Ferrara, Ferrara, Italy gUniversit`a di Firenze, Firenze, Italy hUniversit`a di Urbino, Urbino, Italy
iUniversit`a di Modena e Reggio Emilia, Modena, Italy jUniversit`a di Genova, Genova, Italy
kUniversit`a di Milano Bicocca, Milano, Italy lUniversit`a di Roma Tor Vergata, Roma, Italy mUniversit`a della Basilicata, Potenza, Italy
nAGH - University of Science and Technology, Faculty of Computer Science, Electronics and
Telecommunications, Krak´ow, Poland
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain pHanoi University of Science, Hanoi, Viet Nam
qUniversit`a di Padova, Padova, Italy rUniversit`a di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
The Standard Model (SM) predicts that the photon emitted from the electroweak penguin loop in b → sγ transitions is predominantly left-handed, since the recoiling s quark that couples to a W boson is left-handed. This implies maximal parity violation up to small corrections of the order ms/mb. While the measured inclusive b → sγ rate [1] agrees
with the SM calculations, no direct evidence exists for a nonzero photon polarization in this type of decays. Several extensions of the SM [2], compatible with all current measurements, predict that the photon acquires a significant right-handed component, in particular due to the exchange of a heavy fermion in the penguin loop [3].
This Letter presents a study of the radiative decay B+ → K+π−π+γ, previously
observed at the B factories with a measured branching fraction of (27.6 ± 2.2) × 10−6 [1,4,5]. The inclusion of charge-conjugate processes is implied throughout. Information about the photon polarization is obtained from the angular distribution of the photon direction with respect to the normal to the plane defined by the momenta of the three final-state hadrons in their center-of-mass frame. The shape of this distribution, including the up-down asymmetry between the number of events with the photon on either side of the plane, is determined. This investigation is conceptually similar to the historical experiment that discovered parity violation by measuring the up-down asymmetry of the direction of a particle emitted in a weak decay with respect to an axial vector [6]. In B+→ K+π−π+γ
decays, the up-down asymmetry is proportional to the photon polarization λγ [7, 8] and
therefore measuring a value different from zero corresponds to demonstrating that the photon is polarized. The currently limited knowledge of the structure of the K+π−π+
mass spectrum, which includes interfering kaon resonances, prevents the translation of a measured asymmetry into an actual value for λγ.
The differential B+→ K+π−π+γ decay rate can be described in terms of θ, defined
in the rest frame of the final state hadrons as the angle between the direction opposite to the photon momentum ~pγ and the normal ~pπ,slow× ~pπ,fast to the K+π−π+ plane, where
~
pπ,slow and ~pπ,fast correspond to the momenta of the lower and higher momentum pions,
respectively. Following the notation and developments of Ref. [7], the differential decay rate of B+→ K+π−π+γ can be written as a fourth-order polynomial in cos θ
dΓ ds ds13ds23dcos θ ∝ X i=0,2,4 ai(s, s13, s23) cosiθ + λγ X j=1,3 aj(s, s13, s23) cosjθ , (1)
where sij = (pi+ pj)2 and s = (p1+ p2+ p3)2, and p1, p2 and p3 are the four-momenta of the
π−, π+ and K+ mesons, respectively. The functions ak depend on the resonances present
in the K+π−π+ mass range of interest and their interferences. The up-down asymmetry is
defined as Aud ≡ R1 0 dcos θ dΓ dcos θ − R0 −1dcos θ dΓ dcos θ R1 −1dcos θ dΓ dcos θ , (2) which is proportional to λγ.
The LHCb detector [9] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector
surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system provides a momentum measurement with relative uncertainty that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and impact parameter resolution of 20 µm for tracks with a few GeV/c of transverse momentum (pT). Different types of charged hadrons are
distinguished by information from two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.
Samples of simulated events are used to understand signal and backgrounds. In the simulation, pp collisions are generated using Pythia [10] with a specific LHCb configuration [11]. Decays of hadronic particles are described by EvtGen [12], in which final state radiation is generated using Photos [13]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [14] as described in Ref. [15].
This analysis is based on the LHCb data sample collected from pp collisions at 7 and 8 TeV center-of-mass energies in 2011 and 2012, respectively, corresponding to 3 fb−1 of integrated luminosity. The B+→ K+π−π+γ candidates are built from a photon candidate
and a hadronic system reconstructed from a kaon and two oppositely charged pions satisfying particle identification requirements. Each of the hadrons is required to have a minimum pT of 0.5 GeV/c and at least one of them needs to have a pT larger than
1.2 GeV/c. The isolation of the K+π−π+ vertex from other tracks in the event is ensured
by requiring that the χ2 of the three-track vertex fit and the χ2 of all possible vertices that can be obtained by adding an extra track differ by more than 2. The K+π−π+ mass is
required to be in the [1.1, 1.9] GeV/c2 range. High transverse energy (> 3.0 GeV) photon
candidates are constructed from energy depositions in the electromagnetic calorimeter. The absence of tracks pointing to the calorimeter is used to distinguish neutral from charged electromagnetic particles. A multivariate algorithm based on the energy cluster shape parameters is used to reject approximately 65 % of the π0→ γγ background in which the two photons are reconstructed as a single cluster, while keeping about 95 % of the signal photons. The B+ candidate mass is required to be in the [4.3, 6.9] GeV/c2 range.
Backgrounds that are expected to peak in this mass range are suppressed by removing all candidates consistent with a ¯D0→ K+π−π0 or ρ+→ π+π0 decay when the photon
candidate is assumed to be a π0.
A boosted decision tree [16, 17] is used to further improve the separation between signal and background. Its training is based on the following variables: the impact parameter χ2
of the B+ meson and of each of the final state hadrons, defined as the difference between
the χ2 of a primary vertex (PV) reconstructed with and without the considered particle; the cosine of the angle between the reconstructed B+ momentum and the vector pointing
from the PV to the B+ decay vertex; the flight distance of the B+ meson; and the K+π−π+
] 2 c ) [MeV/ γ π π M(K 4500 5000 5500 6000 6500 ) 2 c Candidates / ( 50 MeV/ 0 500 1000 1500 2000 2500 3000 LHCb
Figure 1: Mass distribution of the selected B+→ K+π−π+γ candidates. The blue solid curve shows the fit results as the sum of the following components: signal (red solid), combinato-rial background (green dotted), missing pion background (black dashed) and other partially reconstructed backgrounds (purple dash-dotted).
The mass distribution of the selected B+ → K+π−π+γ signal is modeled with a
double-tailed Crystal Ball [18] probability density function (PDF), with power-law tails above and below the B mass. The four tail parameters are fixed from simulation; the width of the signal peak is fit separately for 2011 and 2012 data to account for differences in calorimeter calibration. Combinatorial and partially reconstructed backgrounds are considered in the fit, the former modeled with an exponential PDF, the latter described using an ARGUS PDF [19] convolved with a Gaussian function with the same width as the signal to account for the photon energy resolution. The contribution to the partially reconstructed background from events with only one missing pion is considered separately.
The fit of the mass distribution of the selected B+→ K+π−π+γ candidates (Fig. 1)
returns a total signal yield of 13 876 ± 153 events, the largest sample recorded for this channel to date. Figure 2 shows the background-subtracted K+π−π+ mass spectrum determined using the technique of Ref. [20], after constraining the B mass to its nominal value. No peak other than that of the K1(1270)+ resonance can be clearly identified.
Many kaon resonances, with various masses, spins and angular momenta, are expected to contribute and interfere in the considered mass range [1].
The contributions from single resonances cannot be isolated because of the complicated structure of the K+π−π+ mass spectrum. The up-down asymmetry is thus studied inclusively in four intervals of K+π−π+ mass. The [1.4, 1.6] GeV/c2 interval, studied in Ref. [7], includes the K1(1400)+, K2∗(1430)+ and K
∗(1410)+ resonances with small
contributions from the upper tail of the K1(1270)+. At the time of the writing of Ref. [7],
the K1(1400)+ was believed to be the dominant 1+ resonance, so the K1(1270)+ was
not considered. However, subsequent experimental results [21] demonstrated that the K1(1270)+ is more prominent than the K1(1400)+, hence the [1.1, 1.3] GeV/c2 interval is
also studied here. The [1.3, 1.4] GeV/c2 mass interval, which contains the overlap region between the two K1 resonances, and the [1.6, 1.9] GeV/c2 high mass interval, which includes
] 2 c ) [MeV/ π π M(K 1200 1400 1600 1800 ) 2 c Candidates / ( 8 MeV/ 0 50 100 150 200 250 300 350
LHCb
Figure 2: Background-subtracted K+π−π+ mass distribution of the B+→ K+π−π+γ signal. The four intervals of interest, separated by dashed lines, are shown.
spin-2 and spin-3 resonances, are also considered.
In each of the four K+π−π+ mass intervals, a simultaneous fit to the B-candidate mass
spectra in bins of the photon angle is performed in order to determine the background-subtracted angular distribution; the previously described PDF is used to model the mass spectrum in each bin, with all of the fit parameters being shared except for the yields. Since the sign of the photon polarization depends on the sign of the electric charge of the B candidate, the angular variable cos ˆθ ≡ charge(B) cos θ is used. The resulting background-subtracted cos ˆθ distribution, corrected for the selection acceptance and normalized to the inverse of the bin width, is fit with a fourth-order polynomial function normalized to unit area, f (cos ˆθ; c0= 0.5, c1, c2, c3, c4) = 4 X i=0 ciLi(cos ˆθ) , (3)
where Li(x) is the Legendre polynomial of order i and ci is the corresponding coefficient.
Using Eqs. 1 and 3 the up-down asymmetry defined in Eq. 2 can be expressed as
Aud= c1−
c3
4 . (4)
As a cross-check, the up-down asymmetry in each mass interval is also determined with a counting method, rather than an angular fit, as well as considering separately the B+ and B− candidates. All these checks yield compatible results.
The results obtained from a χ2 fit of the normalized binned angular distribution,
performed taking into account the full covariance matrix of the bin contents and all of the systematic uncertainties, are summarized in Table 1. These systematic uncertainties account for the effect of choosing a different fit model, the impact of the limited size of the simulated samples on the fixed parameters, and the possibility of some events migrating from a bin to its neighbor because of the detector resolution, which gives the dominant contribution. The systematic uncertainty associated with the fit model is determined by
θ cos -1 -0.5 0 0.5 1 θ dN/dcos × 1/N 0 0.2 0.4 0.6 0.8 1 LHCb 2 c [1.1,1.3] GeV/ θ cos -1 -0.5 0 0.5 1 θ dN/dcos × 1/N 0 0.2 0.4 0.6 0.8 1 LHCb 2 c [1.3,1.4] GeV/ θ cos -1 -0.5 0 0.5 1 θ dN/dcos × 1/N 0 0.2 0.4 0.6 0.8 1 LHCb 2 c [1.4,1.6] GeV/ θ cos -1 -0.5 0 0.5 1 θ dN/dcos × 1/N 0 0.2 0.4 0.6 0.8 1 LHCb 2 c [1.6,1.9] GeV/
Figure 3: Distributions of cos ˆθ for B+→ K+π−π+γ signal in four intervals of K+π−π+ mass. The solid blue (dashed red) curves are the result of fits allowing all (only even) Legendre components up to the fourth power.
performing the mass fit using several alternative PDFs, while the other two are estimated with simulated pseudoexperiments. Such uncertainties, despite being of the same size as the statistical uncertainty, do not substantially affect the fit results since they are strongly correlated across all angular bins.
The fitted distributions in the four K+π−π+ mass intervals of interest are shown in Fig. 3. In order to illustrate the effect of the up-down asymmetry, the results of another fit imposing c1 = c3 = 0, hence forbidding the terms that carry the λγ dependence, are
overlaid for comparison.
The combined significance of the observed up-down asymmetries is determined from a χ2
test where the null hypothesis is defined as λγ = 0, implying that the up-down asymmetry
is expected to be zero in each mass interval. The corresponding χ2 distribution has four degrees of freedom, and the observed value corresponds to a p-value of 1.7 × 10−7. This translates into a 5.2 σ significance for nonzero up-down asymmetry. Up-down asymmetries can be computed also for an alternative definition of the photon angle, obtained using the normal ~pπ−× ~pπ+ instead of ~pπ,slow× ~pπ,fast. The obtained values, along with the relative fit coefficients, are listed in Table 2.
To summarize, a study of the inclusive flavor-changing neutral current radiative B+→ K+π−π+γ decay, with the K+π−π+mass in the [1.1, 1.9] GeV/c2 range, is performed
Table 1: Legendre coefficients obtained from fits to the normalized background-subtracted cos ˆθ distribution in the four K+π−π+ mass intervals of interest. The up-down asymmetries are obtained from Eq. 4. The quoted uncertainties contain statistical and systematic contributions. The K+π−π+ mass ranges are indicated in GeV/c2 and all the parameters are expressed in units of 10−2. The covariance matrices are given in the supplementary material.
[1.1, 1.3] [1.3, 1.4] [1.4, 1.6] [1.6, 1.9] c1 6.3±1.7 5.4±2.0 4.3±1.9 −4.6±1.8 c2 31.6±2.2 27.0±2.6 43.1±2.3 28.0±2.3 c3 −2.1±2.6 2.0±3.1 −5.2±2.8 −0.6±2.7 c4 3.0±3.0 6.8±3.6 8.1±3.1 −6.2±3.2 Aud 6.9±1.7 4.9±2.0 5.6±1.8 −4.5±1.9
Table 2: Legendre coefficients obtained from fits to the normalized background-subtracted cos ˆθ distribution, using the alternative normal ~pπ−× ~pπ+ for defining the direction of the photon,
in the four K+π−π+ mass intervals of interest. The up-down asymmetries are obtained from Eq. 4. The quoted uncertainties contain statistical and systematic contributions. The K+π−π+ mass ranges are indicated in GeV/c2 and all the parameters are expressed in units of 10−2. The covariance matrices are given in the supplementary material.
[1.1, 1.3] [1.3, 1.4] [1.4, 1.6] [1.6, 1.9] c01 −0.9±1.7 7.4±2.0 5.3±1.9 −3.4±1.8 c02 31.6±2.2 27.4±2.6 43.6±2.3 27.8±2.3 c03 0.8±2.6 0.8±3.1 −4.4±2.8 2.3±2.7 c04 3.4±3.0 7.0±3.6 8.0±3.1 −6.6±3.2 A0 ud −1.1±1.7 7.2±2.0 6.4±1.8 −3.9±1.9
collisions at 7 and 8 TeV center-of-mass energies by the LHCb detector. A total of 13 876 ± 153 signal events is observed. The shape of the angular distribution of the photon with respect to the plane defined by the three final-state hadrons in their rest frame is determined in four intervals of interest in the K+π−π+ mass spectrum. The up-down
asymmetry, which is proportional to the photon polarization, is measured for the first time for each of these K+π−π+ mass intervals. The first observation of a parity-violating photon polarization different from zero at the 5.2 σ significance level in b → sγ transitions is reported. The shape of the photon angular distribution in each bin, as well as the values for the up-down asymmetry, may be used, if theoretical predictions become available, to determine for the first time a value for the photon polarization, and thus constrain the effects of physics beyond the SM in the b → sγ sector.
Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowledge the support received from the ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted towards the communities behind the multiple open source software packages we depend on. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia).
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Supplementary material
The covariance matrices obtained from the fit described in the Letter for both photon angle definitions are shown in Tables 3 and 4.
Table 3: Covariance matrices (in units of 10−3) for the fitted values of c1, c2, c3 and c4 of Table 1, for the four K+π−π+ mass intervals.
[1.1, 1.3] GeV/c2 0.31 0.01 0.47 0.09 0.03 0.68 −0.01 0.16 0.02 0.92 [1.3, 1.4] GeV/c2 0.41 0.02 0.66 0.12 0.04 0.93 0.00 0.20 0.04 1.27 [1.4, 1.6] GeV/c2 0.35 −0.01 0.52 0.14 0.00 0.76 −0.03 0.23 −0.01 0.99 [1.6, 1.9] GeV/c2 0.34 −0.02 0.51 0.08 −0.04 0.75 −0.02 0.15 −0.04 1.01
Table 4: Covariance matrices (in units of 10−3) for the fitted values of c01, c02, c03 and c04 of Table 2, for the four K+π−π+ mass intervals.
[1.1, 1.3] GeV/c2 0.30 0.00 0.47 0.09 0.02 0.68 0.02 0.16 0.02 0.92 [1.3, 1.4] GeV/c2 0.41 0.03 0.66 0.12 0.07 0.93 0.01 0.20 0.10 1.27 [1.4, 1.6] GeV/c2 0.35 0.01 0.53 0.14 0.05 0.76 0.00 0.24 0.03 0.99 [1.6, 1.9] GeV/c2 0.34 0.00 0.51 0.08 0.00 0.75 0.02 0.15 −0.01 1.01
